Electromagnetic induction is the production of voltage across a conductor moving through a magnetic field.
Since an orbiting satellite is passing through the Earth's magnetic field would a voltage be induced in a conductor inside the satellite?
I would expect this voltage to be incredibly small but if true where is this energy "coming from"?
From the kinetic energy of the satellite -- this will make it eventually fall on the Earth surface.
NASA actually experimented with producing current in tethers suspended from the space shuttle. The current generated was sufficient to melt the tether.
In the case of the satellite, there is virtually no power being dissipated so there is no energy being taken from anywhere. When the moving satellite (i.e. conductor) first enters the magnetic field, an electric field is indeed induced, and this causes charge of opposite signs to build on opposite sides of the satellite which quickly creates an opposing electric field, and current ceases to flow.
IF, however, this excess of charge were used to produce current and somehow continuously extract power, then the replenishing of that excess charge would mean a continuous current across the satellite. This would then interact with the magnetic field to produce a force which (by Lenz's law) opposes the satellite's motion and slows it down. Thus, any power generated is drawn from the satellite's orbital energy.
The space shuttle tethers referred to by Humble work like this: current is made to flow across the "satellite" (i.e. the shuttle and the tether), and the excess charge on either end is dissipated through the ionosphere. This explains another important feature: to draw power from the orbital energy you need a net current through the satellite, which is impossible to do with a closed system due to conservation of charge, and like the shuttle you need some external way of dealing with the excess charge.
